Enzymes, a class of proteins, are remarkably well suited for their designated function of accelerating reactions. Naturally occurring enzymes perform this task with great efficiency, enhancing the reaction rates by as many as 17-20 orders of magnitude. Enzymes have been widely used in various laboratory bench work to large scale industrial applications to assist in the increase of desired biochemical and chemical reaction. Enzymes that are efficient or increase the reaction rates by several folds are sought widely for various applications in industry. The rate-enhancement, achieved by enzymes, refers to the ratio of reaction rate that is achieved in presence and in the absence of enzymes.
A number of theories have been proposed for the rate-enhancement achieved by the enzymes. A common aspect shared by these theories is the realization regarding the importance of protein structure—particularly the reaction center or the active-site as shown in FIG. 1. For more than a century, the activity of enzymes has been related to their structure; the “lock-and-key” and “induced-fit” hypotheses have suggested that the structural interactions between enzymes and the substrates play a role in enzyme catalysis. Such a view is incomplete as it fails to explain many aspects of enzyme's biophysical mechanism. In particular, the factors that enable enzymes to provide the large enhancement of reaction rates still remain a mystery.
Recently, an integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active machines and internal protein motions are closely linked to function such as enzyme catalysis (Agarwal, “Enzymes: An integrated view of structure, dynamics and function,” (2006), Microbial Cell Factories, 5:2). This is considerably different from the paradigm that has prevailed in the past, where proteins were considered more or less rigid entities and only the structural interactions between enzyme and substrate was considered important for enzyme function. A number of recent investigations have provided details about the movement of protein parts and their involvement in enzyme function. Techniques such as X-ray crystallography and small-angle scattering, nuclear magnetic resonance (NMR) studies, hydrogen-deuterium exchange, neutron scattering, biochemical and mutational analysis have provided vital clues at individual time-scales. However, the detailed understanding of protein dynamics requires information over a broad range of time-scales. Moreover, the hydration-shell and bulk solvent fluctuations have been suggested to impact protein dynamics, and therefore, protein function. Theoretical studies and computational modeling have provided novel insights into the link between protein dynamics, solvent fluctuations and enzyme catalysis at multiple time-scales.
Evidence has indicated that internal protein dynamics or the internal motions that occur within proteins promote the protein function such as enzyme catalysis and enables the rate-enhancement achieved by enzymes. Referring to FIG. 2, the protein motions occur over a broad range of time-scales and vary considerably in nature. On one hand, there are fast motions in proteins, occurring at 1015 times per second. Harmonic bond vibrations are examples of such motions. On the other hand, concerted global motions referred to as breathing motions, spanning large areas of the proteins, occur about 106 times or less per second. Faster motions are relatively localized to atoms and residues; slower concerted motions often involve larger areas, including distant domains. In between, there are a wide variety of motions involving side-chains, concerted motions of atoms within neighboring residues and loop regions, rocking motions of α-helices and concerted motions of β-strands. These collective motions are thus different from random thermodynamic fluctuations. The concerted movement of protein regions described by a set of atomic displacements for atoms in the protein is collectively referred to as a protein vibration mode.
The protein motions observed by experimental studies depend on the ability of the technique to capture these motions at defined time-scales. X-ray crystallography is able to capture the overall deviations of the protein atoms/residues (indicated by large temperature factor) as well as different orientation of loops and α-helix/β-sheets along sub-states of an enzyme reaction (Petsko, “Not just your average structures”, (1996), Nat. Struct. Biol. 3: 565-566). NMR studies provide an ensemble of structures showing movement of different protein parts, particularly motion of the flexible loop regions at the nanosecond time-scales or longer (Eisenmesser et al., “Enzyme dynamics during catalysis”, (2002), Science 295: 1520-1523; Eisenmesser et al., “Intrinsic dynamics of an enzyme underlies catalysis,” (2005), Nature 438: 117-121). Other techniques including neutron and X-ray scattering, hydrogen-deuterium exchange also provide interesting insights at other timescales. Theoretical and computational techniques have been particularly useful in discovering and characterizing a wide range of protein dynamical events, ranging from picosecond to millisecond and longer time-scale (Agarwal et al., “Network of coupled promoting motions in enzyme catalysis,” (2002), Proc. Natl. Acad. Sci. USA 99: 2794-2799; Agarwal, “Cis/trans isomerization in HIV-1 capsid protein catalyzed by cyclophilin A: Insights from computational and theoretical studies,” (2004), Proteins-Structure Function and Bioinformatics 56: 449-463; Agarwal et al., “Protein dynamics and enzymatic catalysis: investigating the peptidyl-prolyl cis-trans isomerization activity of cyclophilin A,” (2004), Biochemistry 43: 10605-10618; Agarwal, “Role of protein dynamics in reaction rate enhancement by enzymes,” (2005), J: Am. Chem. Soc. 127: 15248-15256).
Enzyme efficiency is understood in terms of how rapidly an enzyme converts the substrates into products. Enzyme rate kinetics describes the modeling of enzyme activity in terms of various factors that influence the conversion of substrate into products. Transition state theory (TST) framework is commonly used for modeling enzyme reactions. In this framework a chemical reaction in the condensed phase (such as enzyme catalysis) may be described in terms of a free energy profile (see FIG. 3).
The free energy profile is generated as a function of a reaction coordinate, which describes the progression of the enzyme reaction. The reaction coordinate can be a single geometrical quantity (internal degree of freedom of the protein) or it could be a collection of various geometrical changes including the protein and the solvent (collective reaction coordinate). The overall rate (kobs) may be expressed as the product of an equilibrium transition state theory rate (kTST), which is directly related to the activation free energy barrier (ΔG), and the transmission coefficient (κ), which accounts for the dynamical re-crossings of the barrier, i.e.,
      k    obs    =            κ      ⁢                          ⁢              k        TST            ⁢                          ⁢      and      ⁢                          ⁢              k        TST              =                  (                                            k              B                        ⁢            T                    h                )            ⁢                        ⅇ                                    -              Δ                        ⁢                                                  ⁢                          G              /                              k                B                                      ⁢            T                          .            
Within this framework, the internal protein dynamics can influence the enzyme catalysis in two distinct ways. First, enzymes are dynamical systems, which have an impact on reaction rates by altering the active-site environment such that more trajectories become productive after successful barrier crossing. FIG. 3 illustrates the behavior of two reaction trajectories close to the transition state (TS). The first trajectory returns to the reactant side (non-productive), while the second trajectory crosses the barrier several times before reaching the product state (productive). Transmission coefficient (κ) is a pre-factor which corrects the TST reaction rate for the number of barrier re-crossings. Secondly, the activation energy barrier (ΔG) can also be decreased by the internal protein dynamics, therefore, impacting the enzyme rate kinetics. Transmission coefficient and activation energy barrier are expected to be different for reaction in the presence and absence of the enzyme. This gives rise to the rate-enhancement achieved by the enzyme.
Recent developments have revealed how the internal protein dynamics is connected to the enzyme mechanism of conversion of substrates to product as well as the rate-enhancement property of enzymes (Agarwal et al, 2004, Biochemistry 43: 10605-10618; Agarwal, 2005, J: Am. Chem. Soc. 127: 15248-15256). Methods have been developed to identify and characterize the slow conformational fluctuations that occur in the enzymes at the time-scale of the reaction. Currently, single computer simulations using molecular dynamics techniques can only model a few nanoseconds (10−9 s); however, the common enzyme reactions occur on microsecond-millisecond (10−6-10−3 s) time-scales. FIG. 4 depicts the use of umbrella sampling technique to sample protein conformations along the various sections of the reaction coordinate using simultaneous molecular dynamics runs. A number of molecular dynamics runs covering the entire reaction pathway are used with biasing potential that allows sampling of higher energy regions. The entire of protein conformations collected can be analyzed by method such as quasi-harmonic analysis (QHA) or related methods to identify the slow conformational fluctuations or the protein vibrational modes corresponding to the microsecond-millisecond time-scales. Further characterization can identify the protein vibrational modes that are closely linked (or coupled) to the enzyme reaction under investigation.
Recent developments have identified the role of protein motions in connection with the rate-enhancement of enzymes. The important protein vibrational modes and the associated enzyme residues form a network of protein vibrations/motions promoting catalysis as depicted in FIG. 5. The role of these dynamical movements and network residues is to provide the thermo-dynamical energy to conduct the reaction. Energy is required to overcome the reaction activation energy barrier, in some enzyme systems this energy is supplied by a chemical source that is coupled to the enzyme reaction such as the hydrolysis of small molecule. However the majority of enzymes (particularly the ones with industrial applications) work without any source of chemical energy to overcome the energy barrier. Energy associated with thermodynamic fluctuations of the solvent surrounding the protein is expected to provide the energy to the active-site. Therefore, thermodynamical coupling between the solvent and the internal protein dynamics plays an important role in enzyme efficiency and rate kinetics. Enzyme shape and its organization of protein residues are closely connected to the transfer of energy from the solvent (regions on the surface of the enzyme molecule) to the active-site (internal region where the biochemical reaction takes place) as shown in FIG. 5.
FIG. 6 exemplifies instances of this network, which extends from surface regions to active site, and is a conserved part of enzyme structure and has a role in promoting catalysis. In FIG. 6 depicts, a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization (PPIase) that has been recently discovered. Theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network indicated that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibration modes has been observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier re-crossings. Modeling and simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network has indicated that protein dynamics plays a role in rate enhancement by enzymes. Similarly the impact of protein dynamics on reaction barrier has been observed. The impact of making enzyme rigid indicates that the activation energy barrier increases, indicating that the dynamically active enzymes are suitable for promoting catalysis and enabling rate-enhancement.
The identified network plays a role in enzyme reaction rate-enhancement by increasing the transmission coefficient. FIG. 7 illustrates a new approach for investigating the effect of protein vibrations on reaction trajectories by adding kinetic energy (KE) to specific parts of the enzyme-substrate complex or the hydration-shell solvent. This approach may be considered analogous to the dynamics reaction path (DRP) method previously used to investigate small chemical systems (Gordon et al., “Interfacing electronic structure theory with dynamics,” (1996), J. Phys. Chem. 100: 11 5 12-1525). In the DRP method, KE is added to one or more of the vibration modes of the system. Originally developed for semi-empirical wavefunctions and subsequently extended by Maluendes and Dupuis, “A dynamic reaction coordinate approach to ab initio reaction pathways: Application to the 1,5 hexadiene cope rearrangement,” (1990), J Chem. Physics 93: 5902-591 1, to ab inito wave functions, DRP was developed to analyze the dynamics of a reaction starting from a TS. In the methods disclosed, KE is added to select protein vibration modes by scaling velocities proportional to atomic displacements indicated in protein vibration mode. The total system energy was kept unchanged by scaling down velocities of the entire system (enzyme, substrate and solvent), according to the following equation:
                              1          2                ⁢                              ∑                          i              =              1                                      N                              enz                ⁢                                  -                                ⁢                subs                                              ⁢                                          ⁢                                    ∑              α                        ⁢                                                  ⁢                                                            m                  i                                ⁡                                  [                                                                                                              (                                                      1                            -                            δ                                                    )                                                                          1                          /                          2                                                                    ⁢                                              v                                                  i                          ⁢                                                                                                          ⁢                          α                                                                                      +                                          η                      ⁢                                                                                          ⁢                                              φ                                                  i                          ⁢                                                                                                          ⁢                          α                                                                                                      ]                                            2                                          +                        1          2                ⁢                              ∑                          i              =              1                                      N              sol                                ⁢                                          ⁢                                    ∑              α                        ⁢                                                  ⁢                                                            m                  i                                ⁡                                  (                                      1                    -                    δ                                    )                                            ⁢                              v                                  i                  ⁢                                                                          ⁢                  α                                2                                                          =                  1        2            ⁢                        ∑                      i            =            1                                N            total                          ⁢                                  ⁢                              ∑            α                    ⁢                                          ⁢                                    m              i                        ⁢                          v                              i                ⁢                                                                  ⁢                α                            2                                            ,in which v represents component of velocity for atom i; mi is the mass of atom; Nenz-subs is the number of solute atoms; Nsol is the number of solvent atoms; Ntotal are total atoms in the system; α represents summation over axes x, y, z; parameter δ represents the amount of energy transferred into the protein vibration mode φ; and η is a variable calculated based on the above equation. Scaled velocities (vn) for atoms were assigned according to following expressions:for enzyme-substrate complex vniα=(1−δ)1/2viα+ηφiα, andfor solvent vniα=(1−δ)1/2viα.
Note that system coordinates are not manipulated. In one example, φ from QHA based on system snapshots from the entire reaction can be used, however, φ obtained from NMA can also be used. Similar methodology can be used for adding KE to the solvent molecules. Atomic velocities of solvent molecules were scaled to increase KE (total system KE was unchanged). Snapshots with increased KE in the protein vibration mode or the surface solvent molecules are propagated using molecular dynamics and observing the real time dynamical trajectory behavior near the TS.
FIG. 7 shows the change in behavior of trajectories with increasing amount of kinetic energy (KE) present in a reaction coupled vibration mode. The protein vibrational modes were identified using quasi-harmonic analysis (QHA) of enzyme conformational along the entire reaction pathway. In TST framework, the alternation in the behavior of the dynamical trajectory with increased KE in a reaction coupled mode suggests that the protein vibrations influence the reaction by increasing the transmission coefficient (κ). It has been observed that not all modes promote the reaction, as indicated by analysis of non-promoting modes. Only a very small number of modes show the reaction promoting effect. Further investigations performed by adding varying amounts of energy to see the effect of these vibrations in a short simulation (pico-second time-scale). The trend indicates that smaller amount of kinetic energy present in these modes, which is expected to be present in real system, promotes the reaction at longer time-scales (hundreds of micro-seconds). The biophysical role of the discovered network in the enzyme reaction can be understood by observing changes. Maximum enzyme stabilization occurs close to the TS (consistent with the TS stabilization theory for enzyme catalysis). The role of the reaction promoting vibrations could, therefore, be interpreted as internal protein dynamical events that facilitate in the stabilization of the TS. Overall, these results indicate that the discovered network of protein vibrations has a promoting effect on the enzyme activity, and is therefore, a factor contributing to rate-enhancement.
The role of hydration-shell solvent in enzyme function may be understood by examining the transfer of KE from first hydration-shell to external regions of protein and its effect on the reaction trajectories were investigated. FIG. 8 shows the results from two representative trajectories propagated after increasing the KE of first solvation shell by 5%; within 0.1 picoseconds an increase in KE of external protein regions is observed. These results indicate transfer of energy from solvent to protein residues; with increase in energy of protein residues more than 8 Å away from the surface occurring within a very short time. This transfer of energy into the protein residues impacts the barrier crossing behavior of reaction trajectories. As depicted in FIG. 9, certain trajectories that are otherwise nonproductive cross barrier within a short time-period and become productive trajectories.
Specifically using the outlined methodology, detailed theoretical studies have lead to the discovery of a network of protein vibrations promoting catalysis in Cyclophilin A. This network is formed by chains of conserved residue and hydrogen-bonds starting from the flexible loop regions on the surface and eventually reaching into the active-site (Agarwal et al., “Protein Dynamics and Enzymatic Catalysis: Investigating the Peptidyl-Prolyl cis/trans Isomerization Activity of Cyclophilin A” Biochemistry 43, pp. 10, 605-10,618 (2004)). Detailed biophysical characterization indicates the role of the dynamical events within this network in the rate enhancement achieved by the enzyme (Agarwal, “Role of Protein Dynamics in Reaction Rate Enhancement by Enzymes,” J. Am. Chem. Soc. 127, pp. 15, 248-15,256 (2005)). The reaction promoting vibrations transfer energy from the bulk solvent to the active-site allowing trajectories to overcome the activation energy barrier. Moreover, these network vibrations enable strongest interactions between enzyme and substrate near the transition state, which is consistent with the view that enzyme function by stabilization of the transition state. The existence of this network is supported by experimental data and has also been confirmed by NMR relaxation studies (Eisenmesser et al., “Enzyme dynamics during catalysis,” Science 295, pp. 1, 520-1,523 (2002); Eisenmesser et al., “Intrinsic dynamics of an enzyme underlies catalysis,” Nature 438, pp. 117-121 (2005)). Cyclophilin A is a member of the prolyl-peptidyl isomerases (PPIases) class of enzymes. Detailed structural analyses of PPIases have indicated that residues and interactions that form the crucial points of this network are conserved across several species. The location of the network residues and interactions within the protein scaffold indicates that promoting vibrations are closely related to the overall shape of PPIase fold.